state of the art in #numerical-methods for ODEs
on 02021-12-05#numerical-methods #ebook by Giray Ökten, CC-BY-NC-SA, using Julia. Root-finding (bisection, Newton’s method, method of secants, Muller’s method (the parabolic version of the method of secants), fixed-point iteration, high-order fixed-point iteration), interpolation (polynomial, Hermite, spline), numerical quadrature and differentiation (Gaussian quadrature), and least-squares approximations. Notably omits matrix algorithms and everything about differential equations: no ODEs, no PDEs. 224 pp. #math
on 02021-12-05Leon Q. Brin’s "Tea Time Numerical Analysis" #numerical-methods #ebook home page (CC-BY-SA). Very good coverage, including historical documents. Starts a bit more basic than the other alternatives. Covers root finding (bisection, fixed-point iteration, Steffensen’s method for accelerating it, Newton’s method, synthetic division, Müller’s method), interpolation (Lagrange polynomials, Neville’s method, Newton polynomials, divided differences, Bèzier curves, splines), quadrature, ordinary differential equations (Taylor methods, #Runge-Kutta, adaptive Runge-Kutta). Includes proofs and error bounds, with more of a mathematical orientation than the alternatives. #math 375 pp.
on 02021-12-05review of #Tea-Time-Numerical-Analysis #numerical-methods textbook #math
on 02021-12-05another #numerical-methods #ebook, this one using Python, including floating-point error, bisection, regula falsi, Newton’s method, the method of secants, numerical optimization including Simpson’s rule, LU factorization, QR factorization, least-squares curve fitting, eigenvalue computation, ODE integration (the midpoint method, #Runge-Kutta, backwards Euler), PDEs (the heat equation and the wave equation), Vandermonde interpolation, Lagrange interpolation, and Chebyshev points #math
on 02021-12-05#numerical-methods #ebook and online courseware; covers least squares, numerical integration of ODE with #Runge-Kutta and #leapfrog-integration; ODEs with boundary conditions; PDEs including elliptic, parabolic, and hyperbolic; successive over-relaxation (SOR); fluid dynamics; Navier-Stokes; Boltzmann’s equation; neutron transport; Monte Carlo techniques, including for radiation transport; etc. #math
on 02021-12-05Sympy supports evaluating Sympy expressions efficiently using native code generation with #Theano, native code generation with f2py and Cython, numpy, and generating Python code. #numerical-methods
on 02016-10-23